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Operator theory

Author: Daniel Alpay
Publisher: Basel : Springer, 2014.
Series: Springer reference.
Edition/Format:   eBook : Document : EnglishView all editions and formats
Publication:Springer Nature Living Reference
Summary:
A one-sentence definition of operator theory could be: The study of (linear) continuous operations between topological vector spaces, these being in general (but not exclusively) Fréchet, Banach, or Hilbert spaces (or their duals). Operator theory is thus a very wide field, with numerous facets, both applied and theoretical. There are deep connections with complex analysis, functional analysis, mathematical  Read more...
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Genre/Form: Electronic books
Material Type: Document, Internet resource
Document Type: Internet Resource, Computer File
All Authors / Contributors: Daniel Alpay
ISBN: 9783034806923 3034806922
OCLC Number: 1111035965
Notes: "Living reference work."
Description: 1 online resource.
Contents: General aspects of quaternionic and Clifford analysis --
Further developments of quaternionic and Clifford analysis --
Infinite dimensional analysis --
Non-commutative theory --
Multivariable operator theory --
Reproducing kernel Hilbert spaces --
de Branges spaces --
Indefinite inner product spaces --
Schur analysis --
Linear system theory.
Series Title: Springer reference.
Responsibility: edited by Daniel Alpay.

Abstract:

A one-sentence definition of operator theory could be: The study of (linear) continuous operations between topological vector spaces, these being in general (but not exclusively) Fréchet, Banach, or Hilbert spaces (or their duals). Operator theory is thus a very wide field, with numerous facets, both applied and theoretical. There are deep connections with complex analysis, functional analysis, mathematical physics, and electrical engineering, to name a few. Fascinating new applications and directions regularly appear, such as operator spaces, free probability, and applications to Clifford analysis. In our choice of the sections, we tried to reflect this diversity. This is a dynamic ongoing project, and more sections are planned, to complete the picture. We hope you enjoy the reading, and profit from this endeavor.

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